Project L.A.B Report

of 42
L.A.B (Learning Arithmetic Basics) | Project Report
PROJECT REPORT
L.A.B
(Learning Arithmetic Basics)
Addition, Subtraction, Multiplication, Division
December, 2014
Prepared for
Teach For Pakistan
www.iteachforpakistan.org
Prepared by
M. Aqeel Ashraf
Fellow-2014
aqeel.ashraf@tfpfellows.org

of 42
1 Transmittal
December 22, 2014
Ms. Maryam Haqqui
Academic Coordinator
Teach For Pakistan, Korangi, Karachi
Dear Madam
Please find enclosed the project report. The report has been drafted on the project
“L.A.B (Learning Arithmetic Basics)”. In this project, four basic arithmetic
operations i.e. addition, subtraction, multiplication and division were taught to
students of grade 3, 4 and 5 at Government Boys Primary School (GBPS), Shireen
Jinnah from 24th Nov to 6th Dec. The report discusses the need of such a project on the
basis of diagnostics assessment results. This is followed by a detailed discussion on
different teaching methodologies applied while teaching above mentioned concepts.
Finally report wraps up on driving conclusions/recommendations based on
comparison between diagnostics and summative assessment results.
Feedback will be appreciated
Kind Regards
M. Aqeel Ashraf
Teach For Pakistan- Fellow 2014
Primary Teacher - GBPS, Shireen Jinnah, Karachi
Email: aqeel.ashraf@tfpfellows.org

of 42
2 Acknowledgment
Author is thankful to
Almighty Allah,
For His unlimited blessings and bounties,
And for keeping him sane, sound and successful;
His parents and co-fellows,
For all their support and trust in him and his aims;
Teach For Pakistan, Training & Support
For teaching him things he knew not;
Shireen Jinnah School Administration,
For their continuous support during his stay at the community and sharing his vision
for his students
And last but never the least
Academic Coordinator
For her utmost help, guidance and time
Which made author able to complete this project

of 42
3 Table of Contents
1 Transmittal 2
2 Acknowledgement 3
3 Table of Contents 4
4 List of Figures 5
6 Abstract 6
7 Introduction – L.A.B 7
7.1 Need & Importance 8
7.2 Unique Features 9
8 Diagnostics Assessment 10
8.1 Design Aspect 11
8.2 Result Analysis 12
8.2.1 Major pitfalls 13
8.2.2 Quantitative Aspect 14
8.3 Conclusion 20
9 Project 21
9.1 Objective 21
9.2 Pedagogy Aspect 22
9.1.1 Peer Learning 22
9.1.2 Minor changes-Bigger Impact 25
9.1.3 Practice / Drilling 26
10 Summative Assessment 27
10.1 Result Analysis 28
11 Comparison- Growth Summary 30
12 Conclusion 40

of 42
4 List of Figures
Figure 1 - A 5th
grader’s response in Mid-term exam 8
Figure 2 - Diagnostic Assessments 10
Figure 3 - 4th Grade- Sample Diagnostic Assessments 11
Figure 4 – Major Pitfalls 13
Figure 5 - Shireen Jinnah-Diagnostic-Histogram 14
Figure 6 - Grade 3,4,5-Diagnostic-Histogram 14
Figure 7 - Shireen Jinnah-Mastery-Diagnostics 16
Figure 8 - Grade 3,4,5-Mastery-Diagnostics 17
Figure 9 - Usual classroom structure 23
Figure 10 - Project L.A.B class view 23
Figure 11 - Peer learning through groups 24
Figure 12 - Learning from Senior Students 24
Figure 13 - Simplified INM of Addition 25
Figure 14 - Practice Worksheet -1 26
Figure 15 - Grade 4-Summative Tests 27
Figure 16 - Shireen Jinnah-Summative-Histogram 28
Figure 17 - Grade 3,4,5-Summative-Histogram 28
Figure 18 - Comparison-Scores-Shireen Jinnah 30
Figure 19 - Comparison-Mastery-Shirren Jinnah 32
Figure 21 - Comparison-Mastery-Grade 3 34

of 42
6 Abstract
Primary purpose of doing L.A.B project was to increase students’ mastery in four basic
numeracy skills namely addition, subtraction, multiplication and division. The need of this
project was felt after analyzing students’ performance in mid-term exams and diagnostic
assessments. Students achieved mere 5.39 marks on average out of 16 in diagnostic tests.
Results showed that about 75% of the students did not have mastery in four basic arithmetic
skills.
Project L.A.B was a 2 week targeted project with a strong growth assessment system. JMP
software was used to analyze the data coming from students. This project used the
technique of making data driven decision to make learning curve steeper for students. Many
new and innovative pedagogy practices were being used to make learning more interesting
and engaging for students. Along with this many old less effective techniques were modified.
After the project, summative test were conducted and results were compared with that of
diagnostics. Results showed that project helped students in a long way in achieving mastery
in these numeracy skills. Mean score increased from 5.39 to 12.4 (out of 16). The results
further highlighted that there is still a big room for improvement in terms of student
mastery.

of 42
7 Introduction- L.A.B
“You cannot create experience, you must undergo it”
Projects-based learning is a dynamic approach where one has a greater control over his learning. As a
Teach for Pakistan fellow, author feels like analyzing/reflecting on these two years of fellowship’s
performance on yearly basis, just gives too less time and opportunity to a fellow to improve and
experiment with different strategies in a classroom setting. So in author’s perspective, it’s more helpful
to divide even single year of fellowship into one-week to two-week time periods and doing
targeted/objective projects with a proper results monitoring system. This was the basic thought in
teaching simple maths concepts like addition, subtraction, multiplication and division under an umbrella
of a project called L.A.B (Learning Arithmetic Basis).
Basic objective of project L.A.B was to increase mastery level of 3rd, 4th and 5th grade students in four
basic arithmetic skills i.e. addition, subtraction, multiplication and division. In order to achieve this
objective, different strategies in all areas were applied and then subsequent outcomes were monitored.
Author has also taught these concepts previously but the mastery level of students as a result was not
impressive. So that experience also served as a reference point while designing L.A.B project.

of 42
7.1 Need & Importance
The need of such a project was strongly felt after the mid-term exams as most of the students were
unable to solve simple problems of addition, subtraction, multiplication and division. Lack of mastery in
these basic arithmetic skills was equally evident across all grade levels. It was necessary to start a
revision camp for these skills with an innovative approach, before moving on to teach higher concepts.
Due to this deficiency, nearly 35% students in each grade level were unable to achieve mere passing
percentage i.e. 33% in Maths mid-term exam.
Figure 1 - A 5th
grader’s response in Mid-term exam
Addition, subtraction, multiplication and division are basic numeracy skills which need to be mastered
in order to achieve minimum mastery on the primary level maths curriculum. These skills will further
make students able to solve basic arithmetic problems of their daily life like doing shopping from a
grocery market, calculating family monthly expenditure etc. This will help students to get engaged with
maths curriculum in more practical way.

of 42
7.2 Unique Features
Author has already taught concepts of addition, subtraction, multiplication and division to 3rd, 4th and
5th graders. So that experience served as a great reference point for author while designing project L.A.B
(Learn Arithmetic Basis). Certain pedagogy strategies that were applied previously went off the list this
time as student demonstrated below average mastery. Innovative and interactive teaching strategies
were chosen after a through debrief session with academic coordinator in order to facilitate student
learning.
Following are the few unique features of the L.A.B project that differentiate it from the way these
concepts were taught in the first attempt.
 Comprehensively designed diagnostic assessments to gauge student understanding of the whole
concept in general and potential pitfalls in particular.
 Incorporating strategies in lesson planning to clarify frequent pitfalls that came up through
diagnostic assessments.
 Following “Learn by Doing” approach in lesson planning to make content more student engaging.
 Applying “Differentiated Learning” strategy in order to make class time equally productive for all
level of students.
 Giving away extra practice worksheets as homework
 Setting ultimate level of mastery as “able to teach others” in order to enhance peer learning and
feedback inside classroom.
 Using charts and other real life items to make content more engaging and appealing.
 Comprehensively designed summative assessments to check student mastery.

of 42
8 Diagnostic Assessments
Diagnostic assessment is a type of assessment which examines what a student knows prior to a learning
program being implemented. Before starting the project, it was necessary to take diagnostic
assessments for following reasons:
 To get information about student's prior knowledge about the concepts.
 To narrow down the points of common misconceptions among students about the concepts.
 To provide a baseline for understanding how much learning has taken place after the project is
completed.
 To plan for appropriate pedagogy and targeted learning to more effectively scaffold the learning
needs of students.
Figure - 2 Diagnostic Assessments

of 42
8.1 Design Aspect
Diagnostics assessments were comprehensively designed in order to gauge students understanding.
They were scaffolded from easy to hard. Furthermore all types of questions related to all rigor level
were included to check both breadth and depth of the student understanding. Copying/cheating during
diagnostics assessments was a major reason of data unreliability which eventually leads to a false
conclusion. To overcome this problem, author designed at least four different diagnostic tests for a
particular grade level and they all were same in their basic layout but different in terms of problems.
Following represents two of the four different diagnostic tests given to fourth graders.
Figure 3 - 4th
Grade- Sample Diagnostic Assessments

of 42
Referring to the diagnostics assessment on the previous page:
“Q#1 (i)” was designed to check student ability to add to different numbers without carrying. Unequal
number of digits in both numbers checked the student knowledge of writing same place value digits
above one another. Next problem i.e. “Q#1 (ii)” was to check student understand of adding numbers
with carrying. Similarly two problems of division were designed in such a way that they must present
every type to case to students for example situation were dividend is less than divisor etc.
Shortcoming: Despite of taking extra care while designing diagnostic assessments, yet one shortcoming
that author came to know later was that multiplication section of these assessments did not checked
the student understanding of multiplying any number with zero.
8.2 Result Analysis
Results from diagnostics assessments were compiled and analyzed in such a way so that they
provide answers to following set questions:
Q#01: What were the most common errors done by students while solving problems?
Q#02: What scores each student scored out of total i.e. 16?
Q#03: How many students in each of the grade have mastered addition, subtraction, multiplication
or division?
Q#04: Calculating common parameter that would help to compare these results with summative
like mean score etc.?

of 42
8.2.1 Major Pitfalls
Following were the major pitfalls / points of misunderstanding as they came up through diagnostics
results:
1. Place value concept: Majority of the students didn’t write
same place value digits one above another while solving
addition & subtraction problems.
2. Knowledge of Signs: Many students did not know the
mathematical signs for addition, subtraction,
multiplication & division.
3. Starting point: Many of the students were starting
solving problems from the left hand side rather than the
right hand side.
4. Concept of carrying: A portion of students did not know
to carry one to the next place value when sum exceeds 9.
5. Concept of borrowing: A portion of students did not knew
to borrow one to the next place value when upper digit
is smaller than the lower one at same place value.
6. Tables: Majority of students have not memorized
multiplication tables. Few of them who did, not actually
knew the rational/logic behind forming those tables.
7. Division: Many of the students failed to identify dividend
and divisor in a division problem.
Misconception # 01
Misconception # 02
Misconception #04
Figure 4 – Major Pitfalls

of 42
8.2.2 Quantitative Aspect
A total of 85 students (after omitting students who either missed diagnostic or summative) were
monitored in this project. This sample size included 33 students, 24 students, 28 students from
grade 3, 4 and 5 respectively. Software used for this purpose was JMP.
Shireen Jinnah - Overall
Figure 5 - Shireen Jinnah-Diagnostic-Histogram
Grade - 3
Figure 6 - Grade 3-Diagnostic-Histogram

of 42
Grade - 4
Figure 6 - Grade 4 --Diagnostic-Histogram
Grade – 5
Figure 6 - Grade 5 --Diagnostic-Histogram
NOTE: A histogram is a display of statistical information that uses rectangles to show the frequency of data items
in successive numerical intervals of equal size. In the most common form of histogram, the independent variable
is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis.

of 42
Shireen Jinnah - Overall
Figure 7 - Shireen Jinnah-Mastery-Diagnostics

of 42
Grade – 3
Figure 8 - Grade 3-Mastery-Diagnostics

of 42
Grade – 4

of 42
Grade – 5

of 42
8.3 Conclusion
Diagnostics result were ALARMING as only 6% (i.e. 6% of 85= 5 students) of the whole Shireen Jinnah’s
students population had mastery in four basic arithmetic skills – addition, subtraction, multiplication
and division. More than 75% of the students at Shireen Jinnah didn’t know subtraction, multiplication
and division. Furthermore results showed that understanding level of student decreased as we go from
addition to subtraction to multiplication to division.
These results confirmed the urgent need of the project L.A.B.

of 42
9 Project L.A.B
9.1 Objective
Following were the objectives of the Project L.A.B (Learning Arithmetic Basis).
Primary objective:
 To increase the mastery level of students in four basic numeracy skills i.e. addition, subtraction,
multiplication and division
Secondary objectives:
 To expose students to a variety of teaching methodologies in order to figure out what works
best for them
 To make author able to track the learning curves of students from start to end of the project
and be able to apply innovative ideas to make this curve steeper.
 Improving author’s understanding of designing diagnostics, INMs (Introduction to New
Material) and summative.
Note: JMP is a statistical analysis software developed by SAS. JMP combines powerful statistics with dynamic
graphics, in memory and on the desktop. Its interactive and visual paradigm enables JMP to reveal insights that
are impossible to gain from raw tables of numbers or static graphs

of 42
9.2 Pedagogy Aspect
Steepness of the learning curve inside classroom depends upon teaching & learning methodologies.
Pedagogy is "how" teaching and learning occurs. Author feels that there must be variety in teaching
methods in order to reach to all the students in the class.
Many new techniques were applied in the L.A.B project so that learning benefits must reach to the
weakest student in class as easily as they reach to the strongest. These techniques focused on extracting
maximum advantage out of the classroom time. Furthermore these teaching methods were designed to
counter the common pitfalls student faced while attempting diagnostics.
9.2.2 Peer Learning
Peer learning is an educational practice in which students interact with other students to attain
educational goals. As these concepts of addition, subtraction and division have been taught earlier. So
this time round the basic thinking behind L.A.B project pedagogy was to make academically weak
students interact with their academically strong peers to achieve required academic goals. Peer learning
was accomplished through following two means;
 Classroom Structure
Previously author used to deliver complete lessons standing in front of the black board and students
going through all the 5 steps of the lesson planning. This approach was proving to be too passive for

of 42
students. Also this approach was making difficult for the
author to quickly spot the students who didn’t get the
concept as lesson was being driven forward mostly by
the correct responses from strong students. So in order
to make the best use of class time and to provide
customized learning solutions for weak students, whole
class was divided into groups of 5 led by an
academically strong student. Author chose 5-6 students
in each grade who were academically strong and made
them leaders of the group. Lesson used to happen in a
way that all students individually listen and comprehend
first two steps i.e. opening and INM (Introduction to
new material) part then they were divided into group
and each group used to start work as an independent
class. Where, first of all, group leader used to repeat
briefly the INM part and then they used to do remaining
three parts of the lesson plan i.e. GP, IP, Exit ticket. In
the meantime, author used to roam in the class and
check the working of different groups. At the end, group
leader present report to the author about how many in their group perfectly got the concept. In this
way, author quickly came to know about the student who didn’t get the concept and then special
combined remedial class were arranged for grade 3, 4 & 5. This technique proved to be really helpful.
Figure 9 - Usual classroom structure
Figure 10- Project L.A.B class view

of 42
 Guest Speakers
Senior students are always a great help for junior students. Author thinks that inter-grade learning
should also happen along with intra-grade learning. That is why during project L.A.B strong students
from upper grade were invited to lower grade classes as guest speakers. They explained one of the
four numeracy skill to the students. This further enhanced peer learning.
HAMMAD (4th grader) L.A.B GroupYOUNUS (4th grader) L.A.B Group
ADNAN (5th grader) explaining addition to 4th gradersMUHAMMAD (4th grader) explaining subtraction to 3rd graders
Figure 11 – Peer learning through groups
Figure 12 – Learning from Senior Students

of 42
9.2.3 Minor Changes – Bigger Impact
There were few basic errors in the way author was delivering his math lessons. Those errors were
corrected while designing lesson plans for project LAB. Amazing results were by doing just these
adjustments. Two of such correction are listed below;
 Improved INM (Introduction to New Material) & Blackboard usage
There were flaws in author’s execution of INM part of lesson plan in class. Basic shortcoming was that
INM was not being translated on the black board in a student friendly mode. Student friendly mode
means that students should be able to take notes of that INM and can refer to them at their homes.
Special attention was given to this aspect and it was made sure that students must take notes of the INM
written on the board. Further it was observed that students at primary level have very short
concentration time. So writing INM in this way helped to pick up from where they left more easily.
Figure 13 – Simplified INM of Addition

of 42
 MATH Notebook
It came to spotlight through diagnostics that students struggled with the concept of place value while
solving problems of addition and subtraction. Majority of the students had that problem. While
brainstorming solutions, it was decided to just change the type of math notebooks students were
using. This small change resulted in solution of a very big misconception. Before this project, student
used to use lined copies for math subject (same as that for Urdu). But now all of the students have
shifted to boxed copies for maths work.
9.2.4 Practice/ Drilling
Maths requires lots of practice and that aspect was
totally absent as students were not revising concept
at home that were being taught in class. During this
project, it was made sure that students solve
numerous problems of addition, subtraction,
multiplication and division. For that many practice
worksheets were given to them that they either
completed at home or at school. This helped them to
memorize the procedure for solving these problems.
Figure 14 – Practice Worksheet -1

of 42
10 Summative Assessment
Summative assessments were used to evaluate student learning and academic achievement at the
conclusion of the L.A.B project.
These tests were used to determine whether students learned what they were expected to learn. In
other words, what makes an assessment “summative” is not the design of the test, per se, but the way
it is used—i.e., to determine whether and to what degree students have learned the material they have
been taught. The design of summative tests were the same as that of diagnostics test with a slight change
as boxed space was provided for student response instead of lined space.
Figure 15 - Grade 4 – Summative Tests

of 42
10.2 Result Analysis
Shireen Jinnah – Overall
Figure 16 - Shireen Jinnah-Summative-Histogram
Grade – 3
Figure 17 - Grade 3-Summative-Histogram

of 42
Grade – 4
Grade – 5

of 42
11 Comparison-Growth Summary
Following statistical visualizations represents the comparison of diagnostics and summative results.
Figure 18 - Comparison-Scores-Shireen Jinnah
Shireen Jinnah

of 42

of 42
Shireen Jinnah – Mastery level - Comparison
Figure 19 - Comparison-Mastery-Shireen Jinnah

of 42
Grade 3

of 42
Grade 3 – Mastery level - Comparison
Figure 20 - Comparison-Mastery-Grade 3

of 42
Grade 4

of 42
Grade 4 – Mastery level – Comparison

of 42
Grade 5

of 42
Grade 5 – Mastery level – Comparison

of 42
12 Conclusion
Based on the results, it was concluded that project L.A.B helped students in a great way in learning basic
numeracy skills. Mastery level of students increased substantially across all grade levels. Students were
exposed to different learning methodologies which made possible for them to approach a particular
concept in number of ways. It was also observed that students having improved understanding of basic
arithmetic skills started to perform better in other concepts like finding HCF & LCM, solving word
problems etc.
Author learned in the process of this project that how to use data to monitor students understanding
level & subsequent growth. It also helped him to learn how to make data-driven decisions to improve
effectiveness.
Another important point that came to spotlight just because of monitoring this data was the number of
students who still didn’t achieve required mastery level for example 31.8% and 43.5% of all the Shireen
Jinnah students didn’t have mastery on multiplication and division respectively as per summative results.

of 42
FEEDBACK

of 42
Plot 333, Korangi Township, Near Pak Refinery | Karachi | Pakistan

Project L.A.B Report

More Related Content

What's hot (20)

Viewers also liked (7)

Similar to Project L.A.B Report (20)

Project L.A.B Report